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The purpose of this paper is to clarify the status of Maxwell's tensor with respect to the virtual power principle (VPP).

Mathematical analysis is employed.

The VPP, logically stronger, is more fundamental. Maxwell's tensor derives from it, under further restrictive assumptions, and hence, its range of applicability is limited. In particular, it fails to deal with some aspects of magnetostriction.

The paper shows that when magnetic constitutive laws depend, locally, on strain, the body force is not, as a rule, the divergence of the Maxwell tensor. People who intend to compute forces this way should be wary of that.

The paper describes how the classical formula of the Maxwell magnetic stress tensor may be extended to cover the magnetostriction phenomena. It is assumed that the ferromagnetic continuum is isotropic and conservative. The method takes into account the magnetic nonlinearity and it assumes that mechanical deflections are sufficiently small to neglect the nonlinearity of the Hooke's law. The paper presents also the experimental method, which has been used to measure the magnetostriction intensity for electrotechnical laminations. As the final result, the distribution of the volume magnetostriction forces acting on the stator core of the induction motor has been calculated.

The expressions of the material derivative of differential forms in the language of vector analysis are introduced. These formulae allow us to describe naturally the electromechanical coupling, and the coupling term appears to be a volume integral. A general approach to compute forces is then proposed, which takes that fact into consideration. The method is applicable in 2D and 3D with dual formulations. Numerical evidences of its efficiency are given.

Discusses the 27 papers in ISEF 1999 Proceedings on the subject of electromagnetisms. States the groups of papers cover such subjects within the discipline as: induction machines; reluctance motors; PM motors; transformers and reactors; and special problems and applications. Debates all of these in great detail and itemizes each with greater in‐depth discussion of the various technical applications and areas. Concludes that the recommendations made should be adhered to.

An algorithm to study a 3D system with rotating field using complex A, A‐V formulation in finite difference solution is presented. Torque calculations are performed using volume Maxwell stress tensor. An eddy current tachometer is investigated. The numerical results are compared with those obtained by measurement.

This paper aims to develop a new 3D analytical model in cylindrical coordinates to study radial flux eddy current couplers (RFECC) while considering the magnetic edge and 3D curvature effects, and the field reaction due to the induced currents.

The analytical model is developed by combining two formulations. A magnetic scalar potential formulation in the air and the magnets regions and a current density formulation in the conductive region. The magnetic field and eddy currents expressions are obtained by solving the 3D Maxwell equations in 3D cylindrical coordinates with the variable separation method. The torque expression is derived from the field solution using the Maxwell stress tensor. In addition to 3D magnetic edge effects, the proposed model takes into account the reaction field effect due to the induced currents in the conducting part. To show the accuracy of the developed 3D analytical model, its results are compared to those from the 3D finite element simulation.

The obtained results prove the accuracy of the new developed 3D analytical model. The comparison of the 3D analytical model with the 2D simulation proves the strong magnetic edge effects impact (in the axial direction) in these devices which must be considered in the modelling. The new analytical model allows the magnetic edge effects consideration without any correction factor and also presents a good compromise between precision and computation time.

The proposed 3D analytical model presents a considerably reduced computation time compared to 3D finite element simulation which makes it efficient as an accurate design and optimization tool for radial flux eddy current devices.

A new analytical model in 3D cylindrical coordinates has been developed to find the electromagnetic torque in radial flux eddy current couplers. This model considers the magnetic edge effects, the 3D curvature effects and the field reaction (without correction factors) while improving the computation time.

The electromagnetic excited audible noise of electrical machines can be mostly attributed to radial forces on stator tooth‐heads. The methodology proposed in this paper uses numerical field simulation to obtain the magnetic air gap field of electrical machines and an analytical‐based post‐processing approach to reveal the relationship between air gap field harmonics and the resulting force wave.

The simulated air gap field is sampled in space and time and a two‐dimensional Fourier transform is performed. The convolution of the Fourier transformed air gap field by itself represents a multiplication in space time domain. During the convolution process, all relevant combinations of field waves are stored and displayed using space vectors.

The effectiveness of the proposed approach is shown on an example machine. Particular examples of individual force waves demonstrate how the approach can be used for practical application in analysis of noise and vibration problems in electrical machines. The proposed method is compared to the result of a Maxwell stress tensor calculation. It shows that the deviation is small enough to justify the approach for analysis purposes.

The combination of analytically understood force waves and the use of numerical simulation by means of air gap field convolution has not been proposed before.

Centres on the decomposition of the total electromagnetic torque of electrical machines for two components. The proposed idea of decomposition relies on the physical meaning of currents that appear in electromagnetic field region. The first torque component acts on external and conduction currents, the second on the material medium particles currents. Proves the main equations with the help of differential Maxwell’s equations. An example has been shown of the calculation of electromagnetic torque components for a synchronous salient‐pole generator.

This paper aims to reviewed analytical methodologies, i.e. lumped parameter magnetic equivalent circuit (LPMEC), magnetic co-energy (MCE), Laplace equations (LE), Maxwell stress tensor (MST) method and sub-domain modelling for design of segmented PM(SPM) consequent pole flux switching machine (SPMCPFSM). Electric machines, especially flux switching machines (FSMs), are accurately modeled using numerical-based finite element analysis (FEA) tools; however, despite of expensive hardware setup, repeated iterative process, complex stator design and permanent magnet (PM) non-linear behavior increases computational time and complexity.

This paper reviews various alternate analytical methodologies for electromagnetic performance calculation. In above-mentioned analytical methodologies, no-load phase flux linkage is performed using LPMEC, magnetic co-energy for cogging torque, LE for magnetic flux density (MFD) components, i.e. radial and tangential and MST for instantaneous torque. Sub-domain model solves electromagnetic performance, i.e. MFD and torque behaviour.

The reviewed analytical methodologies are validated with globally accepted FEA using JMAG Commercial FEA Package v. 18.1 which shows good agreement with accuracy. In comparison of analytical methodologies, analysis reveals that sub-domain model not only get rid of multiples techniques for validation purpose but also provide better results by accounting influence of all machine parts which helps to reduce computational complexity, computational time and drive storage with overall accuracy of ∼99%. Furthermore, authors are confident to recommend sub-domain model for initial design stage of SPMCPFSM when higher accuracy and low computational cost are primal requirements.

The model is developed for high-speed brushless AC applications.

The SPMCPFSM enhances electromagnetic performance owing to segmented PMs configuration which makes it different than conventional designs. Moreover, developed analytical methodologies for SPMCPFSM reduce computational time compared with that of FEA.

The purpose is to implement and compare different approaches for modelling the magnetostriction phenomenon in iron sheet used in rotating electrical machines.

In the force-based approach, the magnetostriction is modelled as a set of equivalent forces, which produce the same deformation of the material as the magnetostriction strains. These forces among other magnetic forces are computed from the solution of the finite element (FE) field computation and used as loads for the displacement-based mechanical FE analysis. In the strain-based approach, the equivalent magnetostrictive forces are not needed and an energy-based model is used to define magnetomechanically coupled constitutive equations of the material. These equations are then space-discretised and solved with the FE method for the magnetic field and the displacements.

It is found that the equivalent forces method can reproduce the displacements and strains of the structure but it results in erroneous stress states. The energy-based method has the ability to reproduce both the stress and strains correctly; thus enabling the analysis of stress-dependent quantities such as the iron losses and the magnetostriction itself.

The investigated methods do not account for hysteresis and other dynamic effects. They also require long computation times. With the available computing resources, the computation time does not present any problem as far as they are not used in everyday design procedures but the modelling of dynamic effect needs to be elaborated.

The developed and implemented methods are verified with measurements and simulation experiments and applied to as complex structure as an electrical machine. The problems related to the different approaches are investigated and explained through simulations.